{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import math\n",
    "import matplotlib.pyplot as plt"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "a = np.array ([0.4000, 0.4439])\n",
    "b = np.array ([0.2439, 0.1463])\n",
    "c = np.array ([0.1707, 0.2293])\n",
    "d = np.array ([0.2293, 0.7610])\n",
    "e = np.array ([0.5171, 0.9414])\n",
    "f = np.array ([0.8732, 0.6536])\n",
    "g = np.array ([0.6878, 0.5219])\n",
    "h = np.array ([0.8488, 0.3609])\n",
    "i = np.array ([0.6683, 0.2536])\n",
    "j = np.array ([0.6195, 0.2634])\n",
    "\n",
    "patterns = [a, b, c, d, e, f, g, h, i, j]\n",
    "# patterns = [a1, b1, c1, d1, e1, j1, k1, a2, b2, c2, d2, e2, j2, k2, a3, b3, c3, d3, e3, j3, k3 ]\n",
    "names = ['a', 'b', 'c', 'd', 'e', 'f', 'g', 'h', 'i', 'j']"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [],
   "source": [
    "def generate_random_weights (signal_tuple_count , cluster_count):\n",
    "    W = np.random.random_sample( size = (signal_tuple_count, cluster_count))\n",
    "    b = -1\n",
    "    W = b * W +1\n",
    "    return W"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "def find_closest_cluster(sample, W):\n",
    "    # sample should be in 1D\n",
    "    sample = np.reshape(sample, (1,sample.size))[0]\n",
    "    D = []\n",
    "    col_count = W.shape[1]\n",
    "    row_count = W.shape[0]\n",
    "    for j in range(col_count):\n",
    "        # j ranging from 0 to col_count-1\n",
    "        d = (sample[0]-W[0][j])**2 + (sample[1]-W[1][j])**2\n",
    "        D = np.append(D, d)\n",
    "    # now D is filled properly\n",
    "    return np.argmin(D)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "def update_weights (W, j, sample):\n",
    "    col_count = W.shape[1]\n",
    "    row_count = W.shape[0]\n",
    "    for i in range(row_count):\n",
    "        W[i][j] = W[i][j] + alpha*(sample[i] - W[i][j])\n",
    "    return W"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "def update_weights_linear (W, j, sample):\n",
    "    col_count = W.shape[1]\n",
    "    row_count = W.shape[0]\n",
    "    if j == 0:\n",
    "        W = update_weights(W, j, sample)\n",
    "        W = update_weights(W, j+1, sample)\n",
    "        W = update_weights(W, col_count-1, sample)\n",
    "    elif j == col_count-1:\n",
    "        W = update_weights(W, j, sample)\n",
    "        W = update_weights(W, j-1, sample)\n",
    "        W = update_weights(W, 0, sample)\n",
    "    else:\n",
    "        W = update_weights(W, j, sample)\n",
    "        W = update_weights(W, j-1, sample)\n",
    "        W = update_weights(W, j+1, sample)\n",
    "    return W"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "def update_weights_diamond (W, j, sample):\n",
    "    col_count = W.shape[1]\n",
    "    row_count = W.shape[0]\n",
    "\n",
    "    left, right, up, down = get_diamond_neighbours(j)\n",
    "    if (left >= 0 and left < col_count):\n",
    "        W = update_weights(W, left, sample)\n",
    "        \n",
    "    if (right >= 0 and right < col_count):\n",
    "        W = update_weights(W, right, sample) \n",
    "    \n",
    "    if (down >= 0 and down < col_count):\n",
    "        W = update_weights(W, down, sample)\n",
    "        \n",
    "    if (up >= 0 and up < col_count):\n",
    "        W = update_weights(W, up, sample)\n",
    "\n",
    "    return W"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [],
   "source": [
    "def get_row_coordinate(j):\n",
    "    return math.floor(j/dim)\n",
    "def get_col_coordinate(j):\n",
    "    return j%dim"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [],
   "source": [
    "def get_diamond_neighbours(j):\n",
    "    dim = 5 #clusters are organized as a 5*5 grid\n",
    "    left = j-1\n",
    "    right = j+1\n",
    "    up = j - dim\n",
    "    down = j + dim\n",
    "    if (get_row_coordinate(left) != get_row_coordinate(j)):\n",
    "        left = -1\n",
    "    if (get_row_coordinate(right) != get_row_coordinate(j)):\n",
    "        right = -1\n",
    "    if (get_col_coordinate(up) != get_col_coordinate(j)):\n",
    "        up = -1\n",
    "    if (get_col_coordinate(down) != get_col_coordinate(j)):\n",
    "        down = -1\n",
    "    return left, right, up, down"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [],
   "source": [
    "def train_one_sample(sample, W, topology):\n",
    "    sample = np.array(sample)\n",
    "    sample = np.reshape(sample, (1,sample.size))[0]\n",
    "    j = find_closest_cluster(sample, W)\n",
    "    if topology == 'none':\n",
    "        W = update_weights(W, j, sample)\n",
    "    elif topology == 'linear':\n",
    "        W = update_weights_linear(W, j, sample)\n",
    "    elif topology == 'diamond':\n",
    "        W = update_weights_diamond(W, j, sample)\n",
    "    return W"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 54,
   "metadata": {},
   "outputs": [],
   "source": [
    "def train(samples, signal_tuple_count, cluster_count, iterations, topology1, topology2, interval):\n",
    "    alpha = 0.6\n",
    "    # generating W matrix randomly\n",
    "    W = generate_random_weights(signal_tuple_count, cluster_count)\n",
    "    \n",
    "    for i in range(iterations):# iterate over epochs\n",
    "        for j in range(len(samples)):# iterate over samples\n",
    "            sample = samples[j]\n",
    "            W = train_one_sample(sample, W, topology1)\n",
    "        # reducing the learning rate\n",
    "        alpha = 0.3 * alpha\n",
    "        if i % interval == 0:\n",
    "            show_plot(W, samples, i)\n",
    "    for i in range(iterations):# iterate over epochs\n",
    "        for j in range(len(samples)):# iterate over samples\n",
    "            sample = samples[j]\n",
    "            W = train_one_sample(sample, W, topology2)\n",
    "        # reducing the learning rate\n",
    "        alpha = 0.5 * alpha\n",
    "        if i % interval == 0:\n",
    "            show_plot(W, samples, i+iterations)\n",
    "    show_plot(W, samples, i+iterations)\n",
    "    return W"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [],
   "source": [
    "def show_plot(W, patterns, iteration_num):\n",
    "    plt.figure()\n",
    "    x, y = W\n",
    "    plt.plot(x,y)\n",
    "    for sample in patterns:\n",
    "        plt.plot(sample[0], sample[1],'x')\n",
    "    plt.title('iteration {}'.format(iteration_num))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 58,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[0.788425  , 0.68866218, 0.6378    , 0.52142206, 0.2439    ,\n",
       "        0.1707    , 0.4       , 0.2293    , 0.5171    , 0.8732    ],\n",
       "       [0.421275  , 0.32222457, 0.259725  , 0.24343235, 0.1463    ,\n",
       "        0.2293    , 0.4439    , 0.761     , 0.9414    , 0.6536    ]])"
      ]
     },
     "execution_count": 58,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "alpha = 0.4\n",
    "dim = 5\n",
    "fW = train(patterns, 2, 10, 1000, 'linear','none',2000)\n",
    "fW"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.7.1"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}
